The effects of inequality on total factor productivityacross districts in South Africa: a spatial econometricanalysis

Delphin Kamanda Espoir . Nicholas Ngepah

� Springer Nature B.V. 2020

Abstract This study builds on the fundamentals of

the new economic geography and the skill-biased

technological change argument, to empirically inves-

tigate whether increasing income/earning inequality

enhances total factor productivity in South Africa. In

so doing, panel data of district-municipalities and

spatial econometric techniques are used for the period

between 1995 and 2015, to gain a better understanding

of the role of location and distance in the effects of

income inequality on total factor productivity. The

results from the analysis and empirical estimations

indicate that: (1) there is strong support for the

existence of positive spatial interactions in the effects

of income inequality on total factor productivity; (2)

the estimated direct effect of income inequality on

TFP in local district-municipalities is negative and

statistically significant, while the indirect effect is

positive and statistically significant as well. These

findings suggest that district-municipalities with mod-

erate levels of inequality and high economic oppor-

tunities, attract more businesses, investments and

important stocks of skilled labour from district-

municipalities with high inequality. Furthermore, the

finding of negative effects supports previous research

suggesting that high levels of inequality set the stage

for the adoption of distortionary policies which

adversely influence the investment climate and pro-

duce political instability, thereby stifling the level of

productivity and growth.

Keywords Income inequality � Total factorproductivity � Spatial econometric � Spillover effects

JEL classification C21 � C23 � D31 � D62 �O47

Introduction

The global economy has not been able to recover

robustly since the 2008 financial crises. Post-crises

output losses have appeared to be persistent even for

countries that were less affected by the crises. Chen

et al. (2019) have shown that among others, long-

lasting capital and total factor productivity shortfalls

relative to pre-crisis trends accounted for the slow, or

lack of recovery. At the same time, developing

countries across the board face key challenges of

poverty and unemployment. South Africa for example

requires an average economic growth rate of above 5

per cent in real terms to be able to effectively tackle its

problem of unemployment and poverty (National

Development Plan 2012).

D. K. Espoir (&) � N. NgepahSchool of Economics and Econometrics, University of

Johannesburg, Johannesburg, South Africa

e-mail: espoirkamandadelphin@gmail.com

N. Ngepah

e-mail: nngepah@uj.ac.za

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https://doi.org/10.1007/s10708-020-10215-2(0123456789().,-volV)( 0123456789().,-volV)

The issue of increasing income inequality and the

effects that its poses on the economic development of

nations has remained one of the most important

preoccupations of development economists and local

and global policy stakeholders. Piketty et al. (2018) in

the world income inequality report have shown that in

2016, the share of total national income for the top 10

per cent earners was 55 per cent in Sub-Saharan

Africa, Brazil, and India, 47 per cent in US-Canada, 46

percent in Russia, 41 per cent in China and 37 per cent

in Europe. Recent results of spatial distribution of

income and wealth, by Solt (2019), indicate the

existence of large income disparities across geograph-

ical regions within countries.

The role of inequality in poverty and marginaliza-

tion is well established. One of the main channels

through which inequality poses a drag on poverty

reduction is its growth-reducing effects. Although

various mechanisms through which inequality affects

growth have been extensively studied both globally

and regionally (Bourguignon 2004; Voitchovsky

2005; Cingano 2014; Ngepah 2016), research on its

effect through total factor productivity is still wanting.

These facts raise questions as to whether and by

how much productivity and economic growth are

associated with increasing income inequality. Are

increasing levels of income inequality good or bad for

productivity and economic growth in an economy?

Are there spatial considerations or spatial spillover

effects in the inequality, productivity and growth

nexus that have been overlooked by previous studies?

Although there is a clear theoretical literature that

explains the mechanism through which inequality

affects productivity and economic growth, empiri-

cally, the question is far from establishing a consensus

among economists. On one hand, a large body of

studies pay attention to the empirical investigation of

the effects of inequality on economic growth by

concentrating on different channels such as endoge-

nous fiscal policy, capital market imperfection and

socio-political instability, yet the empirical findings

often have diverging conclusions. The results of some

empirical models suggest that inequality has a nega-

tive effect on growth (Alesina and Rodrik 1994;

Clarke 1995; Deininger and Squire 1998), while

alternative models suggest that inequality is an

important factor promoting economic growth (Li and

Zou 1998; Forbes 2000; Frank 2008; Pede et al. 2018).

The literature also shows that the differences in

techniques employed to measure inequality, and the

differences in econometric modelling, could have

resulted in large differences in the estimates of the

magnitude of the growth-inequality relationship, sign

and statistical significance (Dominicis et al. 2008). On

the other hand, there is a small but growing body of

empirical literature that focuses on the effects of

inequality on productivity growth. Similar to the

growth nexus, empirical studies on inequality-produc-

tivity nexus have also reported conflicting results.

While some studies have reported negative relation-

ship (Freeman and Medoff 1984; DiPietro 2014),

others have presented positive results on the effects of

inequality on productivity (Mahy et al. 2011).

Despite the controversy in the empirical findings,

both groups of studies have overlooked spatial

considerations that may exist in the relationship,

especially when dealing with data constructed based

on spatial units. Spatial dynamics in inequality have

long been associated with phenomena that bear on

productivity. For exampleMorenoff et al. (2001), have

been able to show that neighbourhood inequalities in

social and economic capacity are consequential for

explaining urban violence. Overlooking spatial effects

in inequality-productivity relationship, if they exist,

might possibly lead to serious bias and inaccuracy in

estimating the true effects of income inequality on

productivity and economic growth. In a case where

spatial effects exist, it should then be appropriate to

provide a complete empirical understanding of their

effects on productivity. This is necessary for two

major reasons. First, the spatial effects might enable

policymakers to better strategize the redistribution of

economic activity, to facilitate aggregate growth and

realize the economic potential of less-developed

geographical regions. Second, the spatial effects might

allow for a more relevant reallocation of available

resources by government. It may also enhance local

institutions by involving community stakeholders and

private sector actors, who are indispensable for spatial

policies to react to the specific challenges and

opportunities encountered in each region.

Therefore, this paper offers a new empirical

evidence of the effects of income inequality on

productivity growth for South Africa. At the end of

the apartheid regime in 1994, real economic growth in

South Africa has averaged just over three per cent per

year. Throughout the time period of rapid economic

growth, which happened between 2003 and 2007, the

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public and private sector have jointly created three and

a half million new jobs. The unemployment rate,

which peaked at 31.2 per cent in 2003, dropped up to

23 per cent in 2007 (Statistics South Africa 2014). The

achievement is attributed to the country’s increase in

total factor productivity (Fedderke et al. 2007). The

growth in total factor productivity (hereafter, TFP)

was shown to have been driven by several new policies

and institutional changes that were implemented

during the start of the democratic period in 1994. In

general, trade liberalization and greater participation

of the private sector were identified as being among

various policies that were deliberately implemented

for higher economic growth (Fedderke et al. 2007).

Table 1 presents some of the existing findings on the

contribution of capital, labour and TFP to the annual

real GDP growth rate before and after the apartheid

period. However, the external economic shock pro-

duced by the international financial crisis of 2008–09

and the country’s structural weaknesses brought

further gains in TFP to an abrupt halt. Much of the

last decade has seen a gradual worsening in employ-

ment gains, factor intensity, TFP growth and the

country’s GDP growth. This situation has recently

opened a debate in the national and international arena

on the question of whether South Africa has the

potential to drive the long-term growth prospects as

outlined in its 2030 National Development Plan

(NDP).

South Africa is reported among the top highest

unequal societies worldwide (World Income Inequal-

ity report 2018). As South Africa remains among the

focal countries that continue to experience the double

challenges of high income inequality and very low

productivity growth, it is crucial to investigate whether

the high levels of inequality affect the current level of

productivity growth. The available South African

literature has provided large and comprehensive

empirical analyses on the level and trends of income

and non-income inequality (Leibbrandt et al. 2001;

Bhorat and Van der Westhuizen 2007; Van Der Berg

2010). However, only a few studies have gone the full

distance in investigating the effects that inequality

poses on productivity and economic growth. Ngepah

(2010) used South Africa’s time-series data from 1993

to 2009 to decompose inequality and investigate the

Kuznets inequality-development hypothesis. Ngepah

(2010) found that production was negatively affected

by the between-group inequality during the study

period. More recently, Akanbi (2016) examined the

growth, poverty and inequality relationship in South

Africa at provincial level, using causality and cointe-

gration techniques. Regarding the effects of inequality

on growth, Akanbi (2016) found bidirectional causal-

ity effects between the two variables. Notwithstanding

the efforts made by these two studies in revealing the

nature and direction of the relationship between

inequality and growth, a review of existing empirical

research indicates that the role of space has not yet

been explored in South Africa, and to our knowledge,

the inequality-productivity relationship has not been

systematically investigated. Most recently, Todesa

and Turok (2018), and Fintel (2018), debated and

decomposed modern spatial inequality in South

Africa, but did not explicitly investigate the role of

space in the effects of inequality on TFP. Clustering

forces might play a significant role specifically in a

society that is characterized by an unequal distribution

of income and economic activity across space.

Based on the abovementioned considerations and

limitations in the empirical literature, this study seeks

to investigate the geographical interactions in the

Table 1 Contribution of capital, labour and TFP to GDP growth, before and after apartheid

Time Period Annual GDP growth Contribution of TFP Contribution of K Contribution of L

Fedderke (2002) 1970s 3.21 - 0.49 2.57 1.17

1980s 2.20 0.34 1.24 0.62

1990s 0.94 1.07 0.44 - 0.58

Arora (2005) 1980–1994 1.20 - 0.40 0.80 0.70

1995–2003 2.90 1.30 0.70 0.90

Source: Arora (2005) and Fedderke (2002)

K, L denotes capital stock and labour, respectively

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inequality-productivity nexus in the context of South

Africa at district-municipality level. In this vein, we

address the following hypothesis: district-municipal-

ities with greater income inequality are more produc-

tive than those with lower income inequality. This

hypothesis is formulated based on the general belief in

skill-biased technological change (henceforth, SBTC)

theory, which links TFP with inequality. According to

the SBTC argument, income or wage inequality

originates from skills differences in workers (Card

and DiNardo 2002; Autor et al. 2006; Risso and

Carrera 2019). Highly skilled workers are liberally

remunerated for their abilities and high productivity.

The SBTC argument clearly states that if earnings

inequality was considerably reduced, productivity

would then drop due to the inefficiencies that would

be generated. As a result, the SBTC argument

considers that income/earning inequality does not

reduce productivity, but boosts it.

In verifying this assumption, this study contributes

to the existing empirical literature in two ways. First,

the study uses a dynamic spatial panel model on a

dataset of district-municipalities from 1995 to 2015,

while paying attention to the role of local district-

municipalities inequality and their effects on TFP of

neighbouring district-municipalities. Compared to

traditional econometric models established on simple

cross-sectional and time-series (CS-TS) data, panel

models, which incorporate spatial features, are more

informative in the sense that they enable not only

better control of unknown heterogeneity factors, but

also the spatial spillover effects (Ragoubi and El Harbi

2018). Second, this research is the first in this field to

investigate whether there are potential direct effects

and spatial spillover effects (indirect effects) in the

relationship between inequality and TFP across

district-municipalities in South Africa, which previous

studies failed to consider. In so doing, we address the

issues of cross-districts’ heterogeneity in a dynamic

spatial panel model by the means of a fixed and

random-effects maximum likelihood estimator (see

Kapoor et al. 2007). Within this framework, we

estimated the unknown regression parameters and

calculated the direct, indirect and total effects of the

changes in TFP due to the changes in income

inequality as documented in Lesage and Pace

(2009). The results from our empirical estimations

indicated that the direct effect of income inequality on

TFP is negative in nature and statistically significant

while the indirect effect (spatial spillover effects) is

positive and statistically significant as well.

The rest of the paper is organized as follows:

‘‘Inequality and productivity: a brief literature

review’’ section presents a brief literature review on

the relationship between inequality and productivity.

‘‘Methodological procedure’’ section stretches the

methodology employed in empirically analysing this

relationship, while ‘‘Data’’ section presents the data.

‘‘Empirical results’’ section presents and discusses the

empirical results and ‘‘Conclusions’’ section con-

cludes by providing key policy suggestions.

Inequality and productivity: a brief literature

review

The recent literature on growth economics is focused

on understanding the factors that drive productivity

and growth within the economy. Among many other

determinants, income inequality is identified as being

part of most explanatory variables (Isaksson 2007).

Since 1989, attention has focused on the long-run

effect of technical change on inequality, and in turn,

the effect of inequality on productivity. In their study

titled ‘‘Credit rationing, tenancy, productivity, and the

dynamics of inequality’’, Braverman and Stiglitz

(1989) indicate that technological change can have

an adverse effect on inequality in the sense that it

reduces the proportion of demand for less-skilled

labour, and that the absolute value of real remunera-

tion to less-skilled workers might decrease. The

authors contend that this is what happens, for example,

when innovation is labour-augmenting (so that one

worker can accomplish the earlier work of five

workers), and that the substitution elasticity between

unskilled labour and other productive factors is very

low. Moreover, Braverman and Stiglitz (1989) use a

general equilibrium theory of land tenancy to show

how changes in technology and in publicly provided

infrastructures that could impact the equilibrium

distribution of land in nations where financial credit

to farmers is rationed. The two authors argue that

when financial credit to farmers is rationed, the

changes in technology can raise the level of inequality

in landholdings, thereby creating a long-run increase

in share tenancy. This in turn may lead to a reduction

in productivity, at least partially offsetting the initial

gains. They then suggested that the only way to

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diminish the probability of these negative effects on

equality and productivity would be the development of

effective rural financial institutions that would operate

with total accountability and under full enforcement

procedures. In the same order of idea, Hanson and

Rose (1997) analyse the effect of non-neutral techno-

logical change on the distribution of income in the

United States, using simulation techniques within a

computable general equilibrium (CGE) modelling

framework. These authors found that labour-augment-

ing technological change causes household income to

increase for all population brackets, but that percent-

age gains were found to be skewed in favour of the

higher ones.

Other theoretical predictions indicate that inequal-

ity could have either negative or positive effects on

productivity and growth. The three main ways in

which inequality could influence productivity and

growth are: physical endowments (credit constraints),

human capital endowments, and through socio-polit-

ical instability channels. In the case where obtaining

financial credit in the capital market is associated with

high cost to the poor due to their lack of collateral,

investment projects that possess return rates that are

below the marginal cost of capital to the poor, can only

be risked by the wealthy. Government policies aimed

at wealth redistribution from the rich to the abjectly

poor may reduce the necessity to borrow and allow the

poor to undertake projects that have affordable rates of

returns. Under this option, redistribution may lead to

higher investment, including higher returns on capital

(Bourguignon 2004; Ngepah 2016). However, several

acknowledged theoretical models (Galor and Zeira

1993; Banerjee and Newman 1993; Galor and Moav

2004) point to information asymmetry as being at the

epicentre of credit market constraints. According to

these models, the development of inequality and

output is determined by the limitations placed on the

poor of occupation choices and investments (both

caused by credit rationing and lack of collateral).

When the poor are limited in making their own

productive investments, then low growth and

high inequality are likely to result. Furthermore,

Voitchovsky (2005) shows that in a Keynesian-type

economy where income levels determine the marginal

rate of savings, rich people situated at the top end of

distribution of income may represent the major source

of savings.

Another important channel of productivity and

growth effects of inequality is human capital endow-

ment. This channel includes education, health, human

ability, skills and training. In cases where ability is

recognized and properly rewarded, there is motivation

for extra efforts and risk-taking. This produces higher

productivity and growth but is accompanied by higher

income inequality. In such situations, talented people

tend to be the beneficiaries of higher earnings simply

for their skills and abilities. In this respect, Hassler and

Mora (2000) indicate that the resulting concentration

of talents, abilities and skills in the advanced technol-

ogy upper-income sector, leads to further technolog-

ical innovation, higher productivity and growth. The

human capital endowment channel is what is known in

the literature as Skill-Biased Technological Change

(SBTC) or the skills-premium theory, which theoret-

ically links TFP to income inequality (Atkinson 1999;

Card and DiNardo 2002). The SBTC theory rests on

the trade-off between equity and efficiency, through

incentivizing the workers. According to the SBTC

argument, income or earnings inequality is a result of

the difference in skills between workers (Autor et al.

2006; Risso and Carrera 2019). Highly skilled workers

are liberally compensated simply for their abilities and

high productivity. The SBTC argument states that if

earnings inequality were considerably reduced, pro-

ductivity would drop because inefficiencies would be

generated. Thus, the SBTC argument considers that

income/earnings inequality does not reduce produc-

tivity, but boosts it. Controversially, other theories

based on ‘fairness’ considerations indicate that earn-

ings compression improves worker relations, encour-

ages cohesiveness, and is thus beneficial to

productivity (Akerlof and Yellen 1990). Ngepah

(2016) concurs, by indicating that the extra rewards

given for skills and talent may offset innovation gains

and productivity due to frustration created in the lower

echelons, resulting from perceived unfairness.

The final channel is the socio-political economy.

This channel would recommend that high levels of

inequality establishes the period for the adoption of

distortionary policies which adversely influence the

investment climate and produce political instability,

thereby stifling the level of productivity and growth

(Persson and Tabellini 1994). This simply means that

in countries where the socio-political instability is

very high and permanent as a result of frustration

created by perceived unfairness, there will be

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substantial movement of business, investment and

labour (high human capital) to more stable countries.

A direct consequence of these movement is that

productivity and growth will decrease in unsta-

ble countries, while increasing in more stable neigh-

boring countries. In the same line of view, Alesina and

Perotti (1996) have equally contended that higher

political instability could originate from high inequal-

ity and produces economic uncertainty, then reducing

investment levels, productivity and growth. In sum,

the channels of physical capital endowment and the

socio-political economy predict that increasing

inequality will reduce productivity and growth, while

the channel of human capital endowment sells the idea

according to which increasing income inequality will

promote productivity and growth.

Few studies have attempted to empirically investi-

gate the productivity-effect of inequality, and existing

evidence in this regard is inconclusive. On the one

hand, some authors have found the effect of inequality

on productivity to be negative and statistically signif-

icant. DiPietro (2014) presents ordinary least square

(OLS) estimations in studying the impact of income

inequality on labour productivity in developing coun-

tries. The author performed regressions that used the

Gini coefficient as a measure of income inequality,

GDP per capita, and average years of schooling. His

findings indicate that income inequality and levels of

development are both significant and negatively asso-

ciated with the labour productivity factor. In respect of

the SBTC argument, Freeman and Medoff (1984)

investigated firm-level productivity and intrafirm

earnings inequality, using a representative sample

group of manufacturing firms in the United States. The

findings of the study show explicitly that reducing

earnings inequality resulted in improved productivity.

Likewise, Kim and Sakamoto (2008) used fixed effects

panel models that control for unobserved productivity

differentials in assessing the net impact of earnings

inequality on productivity, in the United States man-

ufacturing industries from 1979 to 1996. The authors’

findings rejected the SBTC argument that increasing

earnings inequality has enhanced productivity in

recent decades. Lastly, a recent study by Fuentes

et al. (2014) used multivariate statistical analysis to

analyse the long-term effects of technical change on

TFP in developing countries. The authors employed

quintile fixed effect regressions established on a catch-

up process a la Nelson and Phelps (1966). They

controlled for institutional qualities and the distribu-

tion of income, and discovered that income inequality

has a negative effect on TFP in developing countries.

On the other hand, some studies have reported a

positive influence of inequality on productivity. Mahy

et al. (2011) used the Belgian-linked employer–

employee panel data to investigate the relationship

between wage dispersion and firm productivity. The

authors controlled for time-invariant workplace char-

acteristics, simultaneity issues and dynamics in the

adjustment process of productivity. Their results

revealed a positive impact from conditional intra-firm

wage dispersion to firm productivity. Moreover, Galor

and Tsiddon (1997) argue that inequality increases

under the periods of substantial technological pro-

gress. It thus enhances the mobility as well as the

concentration of high-ability workers to manage new

technologies in the most sophisticated sectors, which

results in generating high productivity and growth.

Although the impact of income inequality on

productivity is still an ongoing debate, to our knowl-

edge there is no study that has analysed the role of

spatial interactions in the inequality-productivity

relationship within a country or firm context. The

important role of spatial effects in the relationship

between inequality and economic growth is increas-

ingly being acknowledged in the literature (Pede et al.

2018). As indicated earlier, failing to account for

spatial interactions effects, if they exist, might lead to

serious bias and inaccuracy in estimating the true

effects of income inequality on TFP. Therefore, this

study explores whether there are spatial spillover

effects in the inequality-TFP nexus in South Africa, at

district-municipality level.

Methodological procedure

Econometrics of spatial panel models

Traditional panel data models are developed to

estimate the unknown parameters of a regression

equation with unobserved individual effects. In esti-

mating the coefficients, these models do not take into

account spatial considerations. However, spatial panel

data models address data that contain spatial autocor-

relation and temporal heterogeneity. They account for

these two issues, given that spatial entities and time

periods tend to have spatial or temporal heterogeneity.

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As is shown in the literature, panel data provides a big

simple size, which results in a higher degree of

freedom. The higher the degree of freedom, the more

efficient the estimated marginal effects. Following the

general literature on static panel data, a functional

form with unobserved fixed-effects can be written as

follows:

y ¼ Xbþ ðiT � INÞxþ IT � iNð Þuþ v ð1Þ

where y represents a (NT 9 1) vector of observations

of the dependent variable and X represents a (NT 9

R) matrix of observations of the independent vari-

ables, all of which are assumed to be strictly exoge-

nous. x denotes the unobserved individual effects for

each cross-sectional unity, and u denotes the time-

period effect. The operator iN represents a (N 9 1)

column vector of ones of length N and IN represents an

(N 9 N) identity matrix. The IT operator is an identity

matrix of sizes T 9 T, � is the Kronecker product,

and v is the idiosyncratic error term.

Equation (1) can be estimated by controlling for the

unobserved individual fixed effects. This implies that

an assumption is made that the unobserved individual

effects are time invariant and partially correlate with at

least one of the independent variables. This is known

as the fixed effects (FE) assumption. In this case, the

fixed effect technique is a consistent estimator of the

unknown parameters. Besides the fixed effect tech-

nique, Eq. (1) can be estimated directly using a least

square dummy variable (LSDV), by creating dummy

for the parametersx and u. An alternative solution forEq. (1) is to assume that cross-unit unobserved

individual effects are not fixed, but instead are

unobserved ‘random’ variables which are identically

and independently distributed, x� N (0,r2). This isknown as the random effects assumption. Under this

assumption, the random effects (RE) estimator is

consistent. The major difference between the two

estimators (Fixed and Random effects) lies within the

assumption of the orthogonality ofx. Hausman (1978)

developed a test statistic (a v2 statistic with Q degrees

of freedom) that allows us to determine which,

between the fixed and random effects estimate, is

consistent.

However, in cases where the structures of the data

present spatial autocorrelation, the traditional panel

data models as in Eq. (1), cannot provide consistent

estimates. Nevertheless, the equation can be extended

to account for that spatial autocorrelation. Spatial lag

of the dependent variables, spatial lag of the indepen-

dent variables as well as spatial lag of the errors can be

included. Inclusion of the spatial effects is done by the

predefinition of a standard weighting matrix (Wi;j),

which is constituted by non-negative elements. In a

spatial panel framework, the spatial weighting matrix

is defined in such way that it considers the cross-

sectional relationship as well as the time dimension.

Moreover, the entries in ‘‘Wi;j’’ have different values

depending on whether the neighbourhood concept is

based on the distance between units, or simply on

contiguity. The equation of the spatial weighting

matrix can be presented as follows:

WNT ¼ IT �WN ð2Þ

IT represents a (T 9 T) identity matrix, WN is a

(N 9 N) cross-sectional spatial weighting matrix,

with its diagonal elements set to zero, implying that

no unit can be a neighbour to itself.

In general, there are four kinds of spatial panel

specifications that could be considered: The Spatial

Lag Model (SLM) or Spatial Autoregressive (SAR)

model, the Spatial Error Model (SEM), the Spatial

Autocorrelation (SAC) model, and the Spatial Durbin

Model (SDM). Elhorst (2010) suggests a procedure

starting from general-to-specific to arrive at the most

appropriate econometric model. He suggests that a

panel SDM should be specified and obtain specific

cases by restricting some parameters to zero. Follow-

ing this approach, a panel SDM was opted for this

study. Its choice as a starting point was due to the fact

that it systematically includes the spatial lag of the

dependent and independent variable. We then speci-

fied the panel SDM and included the time lag of the

dependent variable to capture dynamics over the years.

Hence, the SDM is specified as follows:

y ¼ d IT�1 � iNð Þyþ a IT�1 �WNð Þyþ qðIT �WNÞyþ Xbþ h IT �WNð ÞXþ ðiT � INÞxþ IT � iNð Þuþ v

ð3Þ

As in Eq. (1), the parameters in (3) are the same

except d, which captures the marginal effects of the

time lag variable on the dependent variable. q and hrepresent SAR and SAC parameters, respectively.

According to LeSage and Pace (2009), Eq. (3) can

be employed to test two different hypotheses. The first

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is H0: h = 0. This hypothesis examines whether

Eq. (3) can be simplified to a dynamic panel SAR

model. The second is H0:h ? a ? qb = 0, and simply

implies that Eq. (3) can be reduced to a dynamic panel

SEM. The key difference between the dynamic panel

SAR model and the SEM depends on how different

shocks are transmitted throughout the geographical

system. While the first assumes that the value of the

regressor in one geographical entity influences the

dependent variable in a neighbouring entity, the latter

in contrast assumes that the spatial autocorrelation

mechanism works from the idiosyncratic error term.

This means that any random shock in the errors

follows a spatial pattern, which makes the errors

correlate between adjacent entities. To assess these

two null hypotheses, the literature has suggested two

different tests, known as the likelihood ratio (LR), and

Wald tests (Elhorst 2014a, b). In the case where both

hypotheses are rejected, this implies that the true

model that best describes the data is the dynamic panel

SDM (Ragoubi and El Harbi 2018). Conversely,

failing to reject the first null hypothesis implies that

the data are best described by the dynamic panel SAR

model, providing that the robustness tests confirm the

same results. Like the first null hypothesis, if the

second is not rejected, then the true data generating

process would best be described by the dynamic panel

SEM. As shown in Elhorst (2014a, b) and Ragoubi and

El Harbi (2018), a dynamic panel SDM should be

considered if one of these two hypotheses is not

accepted. This is simply because the dynamic panel

SDM contains the characteristics of both dynamic

panel SAR and panel SEM.

1. However, because of the presence of the unob-

served individual fixed effect in Eq. (3), the

Ordinary Least Square (OLS) estimator is not

consistent. Spatial panels FE and RE can be used

to obtain the unknown parameters. Nevertheless,

Eq. (3) is characterized by an intrinsic endogene-

ity problem introduced by the consideration of the

spatial lag of the dependent variable (Wy) and

independent variable (WX), which induces a two-

way causality in the neighbouring relation within

space (Fingleton et al. 2012). Besides this source

of endogeneity, two other sources can be identi-

fied. First, there is a possibility of having one of

the independent variables being endogenous by

nature. Second, the time lag variable which

captures the dynamics over time is also correlated

with the idiosyncratic error term as shown in

traditional dynamic modelling by Blundell and

Bond (2000). To obtain consistent estimates, a

maximum-likelihood estimator (hereafter, MLE)

can be employed, or an instrumental variables

estimator of the type Generalized Spatial Two

Stages Least Square (GS-2SLS), or a Generalized

Method of Moment (Anselin 1988, Kelejian and

Prucha 1998). GS-2SLS estimates are consistent

and robust to non-normality, but not necessarily

efficient. In this study, we utilized the maximum-

likelihood procedure within the FE and RE

framework, as it robustly handles the endogeneity

problems enumerated above and provides more

efficient estimates than the GS-2SLS. The choice

of a dynamic spatial panel with FE and RE can be

made based on the assumption made earlier on the

unobserved individual effects. Thus, one can use

traditional Hausman’s specification test (Hausman

1978) in addition to the Akaike Information

Criteria (AIC) and Schwarz’s Bayesian Informa-

tion Criteria (SBIC), as well as the log likelihood

ratio, to assess if the dynamic spatial panel with

FE is appropriate than RE (Lolayekar and

Mukhopadhyay 2019).

Empirical model

This study empirically constructed a series of regres-

sions to investigate the relationship between TFP

dynamics and the level of income inequality in South

Africa under the skill-biased technological change

(SBTC) hypothesis. Using panel data of South

Africa’s district-municipalities over the period 1995–

2015, we tested whether an increase in the level of

income inequality increases TFP, as supported by the

SBTC argument. We estimated a model and further

tested whether district-municipalities’ idiosyncratic

geographical interactions determine other district-

municipalities’ relationships with TFP dynamics and

the level of income inequality. The empirical function

without spatial interactions is given as follows:

ln TFPi;t ¼ ut þ b1 ln TFPi;t�1 þ b2 lnGinii;tþ b3 ln Tradei;t þ b4 lnHIV=AIDSi;tþ b5 lnEDUCATi;t þ xi þ ei;t

ð4Þ

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where ln TFPi;t denotes TFP at time t and ln TFPi;t�1

is the first period lag. lnGinii;t is the level of income

inequality,ln Tradei;t is openness to trade,

lnHIV=AIDSi;t is the proportion of individual infected

by HIV/AIDS (proxy variable for health) and

lnEDUCATi;t is the level of education. All the

variables are in logarithm form.

Our empirical procedure started by estimating

Eq. (4) using pooled OLS, fixed and random effects,

and System GMM. We then followed by analysing

whether the distribution of income inequality and TFP

is spatially dependent across district-municipalities.

We used the Moran Ii test procedure on the residual of

the OLS regression to assess the possibility of having

spatial interactions in Eq. (4).1 Based on the positive

evidence of spatial dependence in the residual of the

OLS regression, we then extended Eq. (4) by includ-

ing spatial characteristics, and gave the following

system of three equations:

ln TFPi;t ¼ ut þ b1 ln TFPi;t�1 þ h1Wnt ln TFPj;t�1

þ qWnt ln TFPj;t þ b2 lnGinii;t þ h2Wnt lnGinij;t

þ b3 ln Tradei;t þ b4 lnHIV=AIDSi;tþ b5 lnEDUCATi;t þ xi þ ei;t

ð5Þ

ln TFPi;t ¼ ut þ b1 ln TFPi;t�1 þ b2 lnGinii;tþ b3 ln Tradei;t þ b4 lnHIV=AIDSi;tþ b5 lnEDUCATi;t þ xi þ ei;t ð6Þ

Where ei;t ¼ kWnt þ ui;t ð7Þ

ln TFPi;t ¼ ut þ b1 ln TFPi;t�1 þ qWnt ln TFPj;t

þ b2 lnGinii;t þ b3 ln Tradei;tþ b4 lnHIV=AIDSi;tþ b5 lnEDUCATi;t þ xi þ ei;t

ð8Þ

The specification in Eq. (5) is the dynamic Spatial

Durbin Model which extends Eq. (4) by including the

spatial lag of the dependent variable and the spatial lag

of the first period lag of the dependent variable, as well

as the spatial lag of the independent variable of our key

interest (income inequality). Equation (6) is the

dynamic Spatial Error Model (SEM), while Eq. (7) is

the dynamic Spatial Autoregressive (SAR) model. The

specification order of this system of three equations is

very important due to the fact that we began by

considering the dynamic Spatial Durbin Model (SDM)

as suggested by LeSage and Pace (2009) and Elhorst

(2010), and then tested for the significance of the

spatial interaction terms. Hortas-Rico and Rios (2019)

show that the dynamic SEM does not require a

theoretical model for geographical interaction pro-

cesses, as is quite often found for spatial models in

which there are endogenous interactions (SDM and

SAR). Translating these authors’ claims to our case –

for instance, endogenous interactions of income

inequality—could lead to a situation where the vari-

ations in one entity could produce a sequence of

adjustments in all, or in themajority, of other entities in

the sample group, such that a novel long-term steady-

state equilibrium of income inequality could arise.

Consequently, one of the characteristics of the

dynamic SEM specification is that it highlights the

presence of omitted variables reflecting explicit spatial

interactions.

Another important point emphasized in applied

spatial econometrics research is model uncertainty,

which is driven by what is known as the spatial

weighting matrix. The original idea of a spatial

weighting matrix was developed on the concept of

contiguity, according to whichWi;j= 1 if a given entity

i and j are geographically neighbours, and zero if they

are not (Cliff and Ord 1969; Getis 2009). However,

studies have shown that it is a sign of robustness if the

regression results are still consistent with an alterna-

tive definition and specification of W .1 The Global Moran’s Ii statistic was calculated as:

Iin

SF0

Pn

i¼1

Pn

j¼1Wi;j Ri�Rð Þ Rj�Rð Þ

Pn

i¼1ðRi�RÞ2

, where n is the number of obser-

vations (number of district-municipalities). Wi;j is the spatial

weighting matrix of the link between unit i and j. Ri is in our case

the predicted residuals from the OLS regression and R is the

average value of the residuals, R ¼ 1=nPn

i¼1

Ri. Finally SFo is a

standardization factor which assigns all the values of the spatial

matrix an equal weight, i.e. SFo ¼Pn

i¼1

Pn

j¼1

Wi;jRi.

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Data

Estimating total factor productivity and income

inequality

Examining the impact of inequality on TFP requires

TFP scores data as well as inequality indices. To

obtain the TFP scores data, a growth accounting

approach was used. This approach is most commonly

employed in calculating TFP data at a macroeconomic

level of analysis (Hall and Jones 1999; Kalio et al.

2012; Bilgic-Alpaslan 2015; Algarini 2017; Saad

2017). The calculation of TFP under a growth

accounting approach requires data on output, physical

capital, employment and labour compensation

(wages). TFP is then obtained as a simple Solow

residual (Solow 1956). Along the lines of the Solow-

Swan model (see, for example, Barro and Sala-i-

Martin 2004), we therefore specified a production

function using the traditional Cobb–Douglas frame-

work as follows:

Yit ¼ AitCapai;tit Lab

bi;tit 0\ai;t\1 and 0\bi;t\1

ð9Þ

where Yit denotes real output, Ait is the Solow residual

which represents TFPit. Capit and Labit respectively

represent the stock of physical capital and the labour

force. The total number of hours worked is shown in

the literature as the best measure for the labour stock

(Saad 2017). Unfortunately, the lack of data did not

allow us to use this measure and instead, we used the

total number of employed individuals as a proxy for

the labour variable. ai;t and bi;t are unknown param-

eters that represent capital and labour shares respec-

tively. Our interest was in getting data of the level of

TFP. Hence, Eq. (9) was rewritten as follows:

Ait ¼ TFPit ¼Yi;t

CapaitLabbit

ð10Þ

In order to get data on the level of TFP, we logged

both sides of Eq. (10) and gave Eq. (11):

ln TFPit ¼ ln Yit � ða lnCapit þ b ln LabitÞ ð11Þ

From Eq. (11), the level of TFP is calculated by

subtracting the contribution of factor capital and

labour from the level of the real output. However,

the capital and labour shares were unknown param-

eters. We used the information on wages to determine

these two parameters (a and b). We determined the

labour share as the proportion of the total compensa-

tion of the employees to the real output bi;t ¼ wLabitYit

� �.

The wLabit denotes the total labour force compensa-

tion. The low is bi;t, the high is the competition in the

labour market, and the low is wages. We then followed

by determining the capital shares across districts using

the calculated data of the labour shares. The cross

district-municipalities’ capital shares were then

obtained by subtracting to 1 each district-municipal-

ity’s labour shares (ai;t= 1 - bi;t). The data used in

calculating TFP were sourced from Easy Data (Quan-

tec) and the Statistics South Africa databases.2 The

cross district-municipalities’ TFP scores data were

calculated for the period 1995 to 2015.

After calculating the TFP scores’ data per district-

municipality, in the next step, we calculated the degree

of income inequality across district-municipalities.

Available micro-data on individual earnings from the

Post-Apartheid Labour Market Series (PALMS)

dataset enabled us to derive income distributions at

the local level for all district-municipalities.3 The

PALMS dataset is a combination of the Labour Force

Surveys (LFS) and the labour market data from

Statistics South Africa’s October Household Surveys

(OHS). One of the advantages of this dataset is that it

has a large number of observations spanning a long-

time interval, from 1993 to date. This allows the

dataset to be representative at the provincial and

district-municipality levels. Like any other micro-

level database, the PALMS dataset has a few compo-

sitional issues. One of these is that the variable

containing information on individuals’ earnings can-

not be disaggregated up to district-municipality level

for the years 1995, 1998, 2010 and 2012. Therefore, a

reweighting mechanism was implemented in order to

derive a representative sample of earnings at the

district-municipality level. Geographical earning dis-

tributions and selected summary measures could then

be calculated. The PALMS data are exceptionally

2 The data on regional output and GVA, regional capital

formation, employment and labour compensation were sourced

from Quantec easy data (www.easydata.co.za/service/industry-

service-rsa-standardised-industry) and Statistics South Africa

(www.easydata.co.za/service/macroeconomic-service-rsa-

economic-data-stats-sa-national-accounts).3 The PALMS dataset is available at the following link: https://

www.datafirst.uct.ac.za/dataportal/index.php/catalog/434

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qualified to the objectives of this paper; since they are

a unique data source containing comprehensive infor-

mation on earning disparities for South Africa’s

district-municipalities over a time period that covers

the time interval of this study. In addition to this, the

dataset have information on individual earnings which

is more appropriate for analysing inequality in the

context of South Africa due to the fact that wage

income accounts for 70 per cent of income sources in

South Africa and labour income accounts for 85 per

cent of inequality (Leibbrandt et al. 2010). We

calculated the Gini coefficient at the district-munici-

pality level as our measure of income inequality. We

retained the Gini coefficient as our preferred inequal-

ity measure, principally because it is most often used

in the empirical literature of inequality. The Gini index

was therefore defined as follows:

Gini eð Þ ¼ 1� 2 r1

0

L p; eð Þdp ð12Þ

where Gini(e) denotes the Gini coefficient, L(p; e) is

the Lorenz curve of individual earnings, calculated at

probability values of ranked relative cumulated-pop-

ulation. These probability values were defined alge-

braically by the following expression:

p ¼ f zð Þ ) L p; eð Þ ¼ rz

0

ef eð Þ de

dleð13Þ

where p denotes a percentile function, f(z) is the

distribution function determining the share of the

population that have a living standard below or equal

to a certain threshold z and le represents the mean

earning. Note that the Gini coefficient is bounded

between the value zero and one. Generally speaking, a

Gini coefficient of zero implies perfect income

equality. In other words, this suggests that everyone

receives exactly the same amount of income. On the

other hand, a Gini coefficient close or equal to unity

implies very high inequality, suggesting that the

distribution of wealth is concentrated in the hands of

few individuals while the majority remain abjectly

poor. We have presented in Table 2 of ‘‘Appendix 1’’,

the average level of TFP and income inequality for the

52 district-municipalities.

It can be observed from our empirical equations

that we controlled for openness to international trade,

health and education. These variables were chosen as

they are the most suggested control variables for

productivity equations at the macroeconomic level of

analysis (Sequeira et al. 2017). The variable openness

to international trade was measured as the ratio of

import plus export on GDP. For the health variable, we

used the proportion of individuals living with HIV/

AIDS in a given district-municipality to the total

number of the population in that district-municipality.

Contrary to previous studies that have used life

expectancy as a proxy for health in the growth and

productivity equations, in this study, we preferred to

use HIV/AIDS. We believe that HIV/AIDS is more

appropriate and fits well in the productivity model,

because HIV/AIDS has morbidity elements associated

with productivity that cannot be captured by life

expectancy. In the case of South Africa, Ngepah

(2012) showed that the incidence of HIV/AIDS can

determine quality of life, and thus productivity. The

author showed that before the extensive utilization of

antiretroviral drugs, individuals infected with HIV/

AIDS were predestined to die from lack of drugs to

mitigate the effects of the disease. Nowadays, these

individuals may have a long lifespan, but high

morbidity could still influence their productive capa-

bilities. Moreover, Alemu et al. (2005), show that in a

society where the rate of HIV infection is very high,

the average wage increases more slowly than for those

without or with less HIV infection, reflecting the lower

productivity of labour in the presence of the disease.

Finally, we included education, which was measured

as the proportion of employed people in the formal

sector with high and semi-skills, on the total number of

people employed in the formal sector. Education and

health are both part of what is known as human capital.

Instead of constructing a single human capital index

(which was not easily manageable due to data

constraints), we preferred to enter these two variables

separately in the productivity equation, with the idea

of investigating their individual impact on TFP. In

constructing data of all the control variables, different

data sources were used, including Statistics South

Africa (SSA), the South Africa Revenue Service

(SARS), and Easy Data (Quantec).

According to economic theory, the marginal effects

of income inequality are anticipated to be negative.

Even though some inequality is required to offer

incentives for more investment and growth in an

economy, many countries have surpassed the thresh-

old level of inequality with respect to productivity. It

has been shown that when inequality goes beyond the

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optimum level, its effect on productivity growth

becomes negative. It is also expected that the

relationship between TFP and human capital (Educa-

tion) must be positive. In this respect, Zhu et al. (2013)

indicate that human capital (education) impacts TFP

and causes a rise in global competitiveness and

growth. In addition, these authors mention that the

importance of human capital to productivity is not

only for the ability of individuals to employ existing

technology, but for their adaptive capabilities to

manage new technologies and to engage in creative

and innovative activities. Finally, trade openness is

also predicted to positively affect productivity via

export activities, while HIV/AIDS is expected to have

a negative effect on TFP. Coe and Helpman (1995)

show that openness to trade enhances technology

transfer, which in turn leads to TFP growth.

Spatial weighting matrix

As mentioned, a N by N spatial weighting matrix, W,

needed to be generated in order to incorporate spatial

characteristics into the model. The weighting matrix

allowed for defining geographical relationships

between each pair of entities (district-municipalities)

in the analysis. We defined two categories of weight-

ing matrix for the empirical analyses: firstly, an

inverse-distance weighting matrix, where the inverse

of the distances among the geographical district-

municipalities was employed to generate the cell

values of W. We then computed those distances using

geographical data such as the latitude and longitude of

the entities’ centroids. Secondly, the first order

contiguity weighting matrix. Contrary to the first

matrix, which is based on the distance between two

district-municipalities, the second is binary and based

on direct contiguity between a pair of district-munic-

ipalities that share a common border. Moreover, as is

common practice in empirical research, we trans-

formed the initial spatial contiguity weighting matrix

by row-standardizing the values, such that all rows

sum to 1 (Pisati 2001). This strategy allowed not only

to obtain clear interpretations of the outcome, but also

to create proportional weights for all district-munic-

ipalities and avoid bias that could be introduced

because of unequal number of neighbours among

units.

Empirical results

Descriptive statistics

Figure 1 presents the trends of the average level of

TFP and Gini coefficient, as well as their respective

growth rates for the period 1995 to 2015. Between

1995 and 2002, the average district-municipalities’

TFP seems to have increased quickly from negative to

positive values, and remains relatively stable up to

2007. From 2008 to 2012, the trend in the level of TFP

decreases. This decrease is obviously associated with

the economic recession of 2008–2009, which affected

the entire world. However, income inequality is

observed to have marginally increased over time,

and the average value is rounded to 0.6. Over the

years, the growth rate of TFP has, to some extent, co-

evolved with that of income inequality, even though

the changes for both variables are not far from zero.

Table 2 provides descriptive statistics of the variables

used in this research, at their levels and in their growth

Table 2 Descriptive

statistics of the variables

Source: Authors’ own

calculation

VARIABLES Observation Mean Std. Dev Min Max

TFP 1092 0.72 1.19 - 6.21 2.09

GINI 1092 0.61 0.09 0.41 0.94

TRADE 1092 0.57 1.44 0.00 0.69

HIV/AIDS 1092 0.17 0.98 0.00 0.69

EDUCATION 1092 0.57 0.89 0.21 0.43

D TFP 1040 0.18 0.23 - 0.37 2.48

D GINI 1040 0.01 0.08 - 0.36 0.38

D TRADE 1040 0.02 1.03 - 6.95 6.95

D HIV/AIDS 1040 0.01 0.79 - 6.98 3.40

D EDUCATION 1040 0.11 0.59 - 1.17 5.70

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rates. The variables in their levels have greater

dispersion from their means, compared to their

respective growth rate values.

Econometric results

Our empirical procedure begins with the estimation of

Eq. (4) using Pooled Ordinary Least Square (POLS),

Fixed Effects, Random Effects, and the One-step

System GMM. Table 3 presents the estimated results

from these four econometric techniques. We first

focused on the estimated coefficient of Gini, as this

variable measures the direct effects of income

inequality on TFP. As can be seen in Table 3, the

estimated coefficient of Gini is negative and statisti-

cally significant for all the baseline regressions (from

regression 1 to 8). The POLS estimate in regression 2

for instance, is �0:264. This coefficient simply

implies that on average, a 1 per cent increase in the

level of income inequality reduces TFP by 0.3 per

cent. Moreover, the fixed and random effects estimates

(regression 4 and 6) provide estimates of �0:360 and

�0:264, respectively. When controlling for

simultaneity bias between TFP and income inequality

as suggested by Sequeira et al. (2017), the one-step

system GMM (regression 8) provides an estimate of

�0:373. In sum, the average estimated effect of an

increase in income inequality on TFP is �0:373 (from

the GMM), suggesting that increasing income inequal-

ity has a negative and significant effect on TFP across

the 52 district-municipalities in South Africa.

Furthermore, the first period lag of TFP has a

positive and statistically significant effect on the

current values of TFP. This positive effect is in line

with the theoretical expectation which shows that

positive lagged values are likely to produce positive

effects on the current values of TFP, due to persistence

effects (Liu and Bi 2019).

Openness to international trade and Education have

positive and statistically significant effects on TFP

across the 52 district-municipalities. HIV / AIDS was

the only variable found to be statistically insignificant

in the static panel regressions. However, after con-

trolling for endogeneity bias (using GMM) in regres-

sion 8, HIV/AIDS became statistically significant and

exhibited the expected negative sign. The negative

Fig. 1 Evolution of TFP and inequality at district-municipality level in South Africa (from 1995 to 2015)

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effect of HIV/AIDS on factor productivity in South

Africa has previously been documented. Several

previous studies on the effects of HIV on total factor

productivity in Southern African countries have

mentioned this problem. For instance, Alemu et al.

(2005) investigated whether HIV prevalence rates

affect TFP growth on a sample group of over 100

countries, for the time period 1994 to 2002. The

authors examined two Southern African countries

(Lesotho and South Africa). In the case of South

Africa, the authors revealed that HIV/AIDS has a large

negative impact on total factor productivity growth,

where an increase of 1 per cent of HIV infections

reduces TFP by 15 per cent.

Overall, the system GMM estimates were consis-

tent with our initial expectations, as the estimator

addressed the endogeneity problem of income

inequality and provided statistically significant esti-

mates for all the variables. However, we were cautious

in considering the GMM results as definitive for the

inequality-TFP nexus across the 52 district-munici-

palities in South Africa, because we suspected that

there might be some geographical interactions in this

relationship. Hence, we took the analysis a step further

to establish if any spatial dependence existed in the

variables of our key interest (TFP and Gini

coefficient).

Table 3 Results of POLS, fixed and random effects, and system GMM

VARIABLES POLS POLS FE FE RE RE GMM GMM

(1) (2) (3) (4) (5) (6) (7) (8)

lnGini - 0.248* - 0.264** - 0.234* - 0.360*** - 0.248* - 0.264** - 0.0806** - 0.373**

(0.131) (0.131) (0.138) (0.139) (0.131) (0.131) (0.0409) (0.185)

lnlag1TFP 0.475*** 0.457*** 0.461*** 0.433*** 0.475*** 0.457*** 0.781*** 0.681***

(0.0272) (0.0274) (0.0281) (0.0283) (0.0272) (0.0274) (0.0511) (0.0608)

lnTrade – 0.0310** – 0.0507*** – 0.0310** – 0.0973***

(0.0122) (0.0177) (0.0122) (0.0364)

lnHIV/AIDS – - 0.0282 – - 0.0327 – - 0.0282 – - 0.205***

(0.0179) (0.0203) (0.0179) (0.0501)

lnEDUCAT – 0.0474*** – 0.127*** – 0.0474*** – 0.0864**

(0.0180) (0.0294) (0.0180) (0.0407)

Constant - 0.0767 - 0.378** - 0.0690 - 0.988*** - 0.0767 - 0.378** – –

(0.0680) (0.186) (0.0716) (0.262) (0.0680) (0.186)

Observations 1092 1092 1092 1092 1092 1092 1092 1092

R-squared 0.219 0.232 0.206 0.229 0.219 0.232

Hausman test (v2) 17.24***

[0.004]

Wald v2 243.69 281.57

AR(1) - 10.61 - 9.34

AR(2) 1.58 1.08

Sargan statistic 140.38*** 131.2***

[0.000] [0.000]

Standard errors in parentheses, ***p\ 0.01, **p\ 0.05, *p\ 0.1

The Hausman test is performed for regression (4) and (6). H0: RE is appropriate

P-values in []

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Fig. 2 Spatial distribution of income inequality across South African district-municipalities (1995 and 2015). Source: Authors self-

painting using PALMS dataset

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Preliminary analysis of the role of space

With the purpose of providing a first analysis of the

geographical pattern of the distribution of inequality at

the local level, Fig. 2 presents plots of the contour map

of the Gini coefficient across the 52 South African

district-municipalities. The map displays substantial

spatial disparities of income inequality, ranging from

low coefficients of 0.48 for 1995 and 0.58 for 2015, to

high coefficients of 0.65 for 1995 and 0.78 for 2015.

The geographical distribution of income inequality in

South Africa is complex, since perceptible spatial

clusters of very-high and very-low income inequality

portray this.

Figure 3a and b present the Moran’s Ii scatter plots

of the residuals obtained from OLS regressions as

suggested by Anselin et al. (1996). The plots aim to

provide additional evidence on the spatial clustering in

the residuals of the effects of inequality on TFP across

the 52 South African district-municipalities. The plots

of the Moran’s Ii were obtained using contiguity

weight matrix. The plotted residuals were obtained

fromOLSmodels that included the Gini coefficient for

the independent variables, and the temporal lag of

Fig. 3 a Moran scatter plot (Moran’s I = 0.344), Global Spatial Autocorrelation, 1995. Red line: Fitted line. b Moran scatter plot

(Moran’s I = 0.462), Global Spatial Autocorrelation, 2015. Red line: Fitted line

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TFP, for the years 1995 and 2015. The oblique red line

is a fitted linear regression curve which represents the

degree of spatial correlation in the residual of the TFP-

inequality relationship. We employed Monte Carlo

randomization to evaluate the significance of the

Moran’s Ii coefficient. The results of the Moran I test

revealed statistically significant coefficients of 0.344

for the year 1995, and 0.462 for the year 2015. The

significance of these statistics implies that there are

spatial interactions in the residual of the effects of

inequality to TFP. The Moran scatter plots are divided

into four different quadrants, which represent four

different types of spatial interactions among the

district-municipalities:

(1) The first quadrant (on the upper right) contains

the spatial clustering of district-municipalities

with high TFP, and are bordered by district-

municipalities with high TFP (high-high). This

means that those locations are associated with

positive values of spatial relationship.

(2) The second quadrant (on the upper left) indi-

cates that the clustering of low TFP district

municipalities is surrounded by district-munic-

ipalities that have high TFP (low–high). This

means that those particular locations have

negative values of spatial association.

(3) The third quadrant (lower left) displays spatial

clustering of district-municipalities with low

TFP that have low TFP district-municipalities as

neighbours (low-low). These locations are allied

with positive values of spatial association.

(4) Quadrant 4 (lower right) displays spatial clus-

tering of high TFP district-municipalities sur-

rounded by district-municipalities with low TFP

(high-low). These locations are associated with

negative values of spatial interactions, as in

quadrant 2.

Even though positive clustering around high TFP

seems to dominate in Fig. 3a and b, it is clear that

positive assembling around low TFP also occurs in the

two plots, and seems statistically significant. The

noticeable slopes in Fig. 3a and b as well as the higher

number of units in the lower-left and upper-right

quadrants, provide some indication of the importance

of the effects of spatial interactions in the relationship

between inequality and TFP. Another observation to

be mentioned is that the spatial clustering in both

highly populated quadrants includes district-munici-

palities from different provinces of South Africa i.e.

Eastern Cape, Free State, Kwazulu-Natal, Limpopo,

Mpumalanga, North West and Northern Cape, and

these tend to cluster around high spatial TFP effects,

whereas Gauteng and Western Cape tend to cluster

around low spatial TFP effects. Nevertheless, it is not

surprising that the district-municipalities in the North

West, Northern Cape and Limpopo provinces are

among the most prevalent in the quadrant where TFP

presents the lowest spatial interaction effects. These

are among the provinces in which there is a lesser

concentration of economic activity, possibly due to

historical factors. In addition, they are among the

provinces where the share of the top 10 per cent of

earners’ wages compared to the share of the bottom 40

per cent, almost doubled (from 5.11 to 10.13) during

the period 1995 to 2014 (World Bank assessment

report 2018). Table 11 (in ‘‘Appendix 2’’) presents

further information on local clustering by investigat-

ing the Moran Ii statistic for each district-municipal-

ity. The results in Table 11 are for the regression

residuals controlling for the two independent vari-

ables, as in Fig. 3a and b (above).

Overall, the results of the plots of the Moran Ii for

the two extreme periods of the time span of this study

(1995 to 2015), showed evidence of spatial concen-

tration in the residual of the inequality-TFP relation-

ship across district-municipalities in South Africa.

Additionally, the scatter plots produced by using an

inverse distance weighting matrix (results not reported

but available upon request) revealed similar results of

Table 4 Results of robust Lagrange multiplier

Spatial lag Spatial error

Weight type: Row-standardized first-order contiguity

Model type

No temporal lag 63.482 - 2.7e ? 14

With temporal lag 134.054*** 118.897***

Weight type: Inverse-distance

Model type:

No temporal lag 1.6e ? 13*** 1.6e ? 13***

With temporal lag 1.4e ? 04 1.3e ? 04***

***P\ 0.01, **P\ 0.05 and *P\ 0.1

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patterns of spatial concentration. These results have

two important methodological implications. First,

they imply that earlier inequality-productivity studies

based on non-spatial models are inappropriate.

Second, if our study had not taken into account this

evidence of spatial concentration (as in Table 3), we

would have under- or overestimated the effects of

income inequality on TFP in South Africa. After

having established evidence of spatial autocorrelation

in the data, we then focused on establishing which type

of spatial model would be empirically appropriate. We

assessed whether a dynamic spatial lag or a dynamic

spatial error model would efficiently explain the true

data generating process of this study, or whether we

should consider a dynamic spatial Durbin model. In

Table 4 we present the statistic values of the Robust

Lagrange Multiplier (RLM) for both spatial lag and

spatial error interactions. The statistics were computed

on the residuals of OLS models that used the Gini

coefficient and the temporal lag of TFP as regressors.

For robustness assessment in the results, the RLM

statistics were calculated using the two weighting

matrices (first order contiguity and inverse-distance).

As mentioned, Ragoubi and El Harbi (2018) show that

if a spatial lag effect is detected when a spatial error

effect is also present in the model, one should consider

the SDM as the appropriate specification for the data.

In addition, a likelihood ratio andWald tests should be

conducted to confirm the validity of the estimates of

the SDM. Globally, the results of the RLM tests reject

the null hypotheses of no spatially lagged dependent

variable and no spatially clustered error term. The

results then clearly show that the most suitable empir-

ical specification should include the inverse-distance

weights and a dynamic spatial Durbin.

Empirical results of spatial specification

The results of the dynamic spatial panel specifications

are presented in Tables 5 and 6. For both tables, the

results were obtained using the inverse-distance

weighting matrix. In Table 5, we present a baseline

estimation of Eq. (8). All estimates were obtained

using a Fixed and Random Effects Maximum Like-

lihood estimator. The first and third regression in

columns one and three of Table 5 are restricted models

of the spatial specification in Eq. (8). In addition to the

spatially lagged values of TFP, these two columns

include the values of the current Gini coefficient of a

local district-municipality, the first period lag of TFP,

the spatially lagged values of the Gini, and the

spatially lagged values of the first period lag of TFP.

Columns two and four contain estimates of the full

specification of Eq. (8), where the rest of the control

variables are included (Openness to international

trade, HIV/AIDS and Education). We implemented

an F-test to assess the joint significance of the three

control variables included in the unrestricted models

(2 and 4). The result of the F-test in Table 5 concludes

that the three control variables taken together have a

statistically significant effect on TFP.

Although the estimates in columns one and three

are statistically significant and show that geographical

interaction effects are important and should be taken

into account, for evaluation purposes we considered

the estimates in columns two and four as the main

outcome. This was not only for the fact that these

columns are consistent with the specification in

Eq. (8), but also for the observation that their

estimates are stable. The baseline estimations indicate

substantial difference between the estimates obtained

and presented in Table 3 (the dynamic POLS, Fixed

and Random Effects, system GMM), and those

presented in Table 5 (dynamic Fixed and Random

Effects Spatial Durbin Maximum Likelihood

Estimators).

The estimated coefficients of the variable Gini

presented in Table 3 have much lesser magnitude

compared to those in Table 5. This means that non-

spatial models underestimate the real effects of

income inequality on TFP in South Africa. However,

the results of the effects of income inequality on TFP

were found statistically significant, with the expected

negative sign. The estimated coefficients are - 0.743

and - 0.469 respectively for the temporal SDM-FE

(regression 2) and SDM-RE (regression 4). This

implies that an increase in income inequality reduces

TFP at district-municipality level in South Africa. All

the regression results of Table 5 indicate that the

estimated sign of the coefficient of Gini is negative,

which is opposite of the theoretical prediction of the

SBTC view. In sum, none of the regression results in

Table 5 provide any support for the hypothesis that

increasing inequality has a positive impact on TFP.

Our finding of negative impacts of income inequality

on TFP is in line with those of Kim and Sakamoto

(2008) and DiPietro (2014). These authors indicate

that, when inequality is beyond the optimum level, its

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effect on growth of productivity becomes negative.

This argument seems to be validated in the case of

South Africa. One of the plausible reasons explaining

why inequality could negatively affect TFP in South

Africa, is that most district-municipalities have sur-

passed the bar on the average level of income

inequality of 0.465 for Sub-Saharan African countries

(Nel 2003). When inequality levels are beyond this

average point, an increase of one standard deviation is

predicted to have a negative effect on economic

growth. Nel (2003) indicates that not all levels of

inequality are necessarily bad for economic growth.

Table 5 Main results: dynamic fixed and random-effects MLE (spatial weight: inverse-distance)

VARIABLES Temporal SDM-FE (1) Temporal SDM-FE (2) Temporal SDM-RE (3) Temporal SDM-RE (4)

lnGini - 0.743*** - 0.743*** - 0.434*** - 0.469***

(0.199) (0.199) (0.132) (0.135)

lnlag1TFP 0.253*** 0.251*** 0.278*** 0.275***

(0.0300) (0.0300) (0.0291) (0.0290)

lnTrade – 0.0271* – 0.0247**

(0.0165) (0.0113)

lnHIV/AIDS – 0.00304 – - 0.00197

(0.0190) (0.0166)

lnEDUCAT – 0.0521* – 0.0272

(0.0281) (0.0177)

W * lnGini (h2) 0.714*** 0.615*** 0.123 0.173

(0.291) (0.296) (0.100) (0.106)

W * lnlag1TFP (h1) 0.355*** 0.340*** 0.344*** 0.332***

(0.094) (0.094) (0.092) (0.092)

W * lnTFP ðqÞ 0.413*** 0.401*** 0.411*** 0.402***

(0.080) (0.081) (0.079) (0.079)

Constant – – - 0.149** - 0.437**

(0.0652) (0.173)

Observations 1092 1092 1092 1092

Pseudo R2 0.288 0.313 0.310 0.318

Model Selection tests

Log likelihood - 839.47 - 836.43 - 868.59 - 864.68

AIC 1690.96 1690.86 1753.18 1751.36

SBIC 1720.93 1735.82 1793.15 1806.31

Wald v2 model sign 524.11 532.71 551.17 562.56

Wald test spatial term 200.42*** 172.08*** 189.57*** 177.33***

[0.000] [0.000] [0.000] [0.000]

r2e 0.540*** 0.539*** 0.534*** 0.532***

F-test joint sign (0.011) (0.011) (0.011) (0.011)

Hausman test (v2) 7.58** 7.12**

[0.05] [0.06]

SDM-FE (2) v/s SDM- RE (4) 16.46***

[0.005]

Standard errors in parentheses, ***p\ 0.01, **p\ 0.05, *p\ 0.1

P-values in []

Hausman test H0: Temporal SDM-RE is consistent

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The author shows that there could be a positive

relationship between inequality and growth, as long as

the Gini coefficient remains below a threshold point of

0.40. Moreover, Cornia and Court (2001) are of the

belief that there might be a lower bound of 0.25,

beyond which too much income ‘‘equality’’ becomes

harmful for productivity and growth. They argue that

such equality levels are associated with wide-spread

free-riding, labour shirking, incentive traps and high

supervision costs. For these two authors, the ‘‘opti-

mal’’ inequality levels lie between the interval of 0.25

and 0.40. However, the problem of South Africa’s

district-municipalities is that most of them have

inequality levels higher than the 0.40 point (the

average in our sample group is 0.61—see Table 2).

Another additional reason that could explain why

inequality might negatively affect TFP in South Africa

is the shift of income shares from the poor classes to

the rich. These income shifts might have created the

recent socio-political tensions among races, and the

recent political assassinations and xenophobic attacks,

which in turn might have negatively affected produc-

tivity and growth.

The debate regarding the presumed effect of

inequality on political instability and on productivity

and growth is of great importance in the South African

context, where existing evidence indicates that polit-

ical instability is a key obstacle to high economic

growth (see for instance Fedderke and Luiz 2008). We

have provided additional support to the result of the

marginal negative effect of inequality on productivity

by briefly exploring the channel of political economy.

As mentioned earlier, income inequality is said to

foster political instability, which in turn harms

productivity and economic growth. Following Nel

(2003), we have presented a simple linear regression

between political instability and income inequality,

with a theoretical expectation of a positive relationship

between the two variables. We used the regional

number of public violence as a proxy for political

instability (see IHS regional explorer database), and

Gini coefficient for income inequality. The choice of

public violence as a proxy for political instability is

justified by the fact that rising public violence is shown

to be positively related to political instability (Fed-

derke and Luiz 2008). The results of this regression are

reported in Table 9 of ‘‘Appendix 1’’. They show that

income inequality has positive and statistically signif-

icant effects on political instability in South Africa,

and indicate that, in average, polities with high income

inequality levels are less stable than those with lower

levels of income inequality. This fosters perceptions

that the South African government is strongly influ-

enced by these levels of inequality, which dispose it to

political instability. Such perceptions influence the

decisions of domestic and foreign investors and

impact the growth prospects of the more unequal

district-municipalities. In addition to this, in Fig. 4

(‘‘Appendix 1’’), we presented a two-way scatter plot

between the variable public violence and Gini. The

fitted values exhibited an increasing trend which in

fact support the positive relationship obtained from the

OLS regression.

Before we examined the estimates of the rest of the

control variables and the spatially lagged variables, we

econometrically assessed the most efficient regression

Table 6 Results of the

cumulative marginal long-

run effects

Standard errors in

parentheses, ***p\ 0.01,

**p\ 0.05, *p\ 0.1

The marginal effects are

calculated using the Delta

Method

VARIABLES Direct effects Indirect effects Total effects

lnGini - 0.743*** 0.436*** - 0.300***

(0.199) (0.333) (0.268)

Lnlag1TFP 0.251*** 0.607*** 0.867***

(0.0300) (0.075) (0.073)

lnTrade 0.0271* 0.015 0.042

(0.0165) (0.010) (0.025)

lnHIV/AIDS 0.00304 0.001 0.004

(0.0190) (0.010) (0.029)

lnEDUCAT 0.0521* 0.028 0.081*

(0.0281) (0.017) (0.044)

Observations 1092 1092 1092

Number of groups 52 52 52

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between the temporal SDM-FE (2) and SDM-RE (4).

We used different statistics to test the assumption that

the cross-districts’ unobserved fixed effects better fit

the data than the random effects. The first statistic used

for this comparison was the traditional Hausman test,

the results of which can be seen in Table 5. This

statistic suggests that the random effects are rejected at

the 1 per cent significance level, and that the SDM-FE

is more appropriate. Besides the Hausman statistic, we

calculated two additional statistics that are often used

for model choices: the log likelihood and the AIC and

SBIC statistics. The two additional test statistics are

seen by Anselin (2005) as measures for goodness of fit

for the spatial panel regression models. Ragoubi and

El Harbi (2018) contend that the random effects model

converges to its fixed-effects counterpart if its log

likelihood statistic is lower than that of the fixed-

effects. Additionally, when the AIC and SBIC statis-

tics are used for model selection, it is well known that

the model with the lowest statistic will be the most

efficient (Lolayekar and Mukhopadhyay 2019). The

results of these two additional tests are also presented

in Table 5. For the log likelihood, we found that the

random effects model had the lowest statistic, imply-

ing that the fixed-effects model is the most efficient.

Moreover, the results of the AIC and SBIC show that

the fixed-effects model has the lowest calculated

statistics, indicating that the fixed-effects model is

efficient. In sum, the results from the AIC and SBIC

corroborate those obtained from the Hausman test and

from the log likelihood. It is worth noting that the

SDM-FE is robust and yields reliable results, as

demonstrated by these different traditional measures

of goodness-of-fit. Consequently, we based the eco-

nomic interpretation of the results of the control

variables on the temporal SDM-FE model.

The estimated coefficient on the spatially lagged

dependent variable (q) was found to be positive and

statistically significant at the 1 per cent level of

significance. The positive and statistically significant

q simply shows that the average level of TFP in

contiguous district-municipalities has a positive influ-

ence on local innovative activities. Moreover, the

estimated coefficient on the spatially lagged Gini

variable was also found to be positive and statistically

significant at the 1 per cent level of significance. This

indicates that the level of income inequality in

neighbouring district-municipalities has a positive

effect on local TFP. This positive effect may seem

strange but is not surprising in the context of South

Africa, because in most district-municipalities where

the average level of income inequality is relatively

high, there are less economic opportunities. As a

result, there are substantial movements of businesses,

investments and labour across borders in search of

new economic opportunities. These flows also involve

important stocks of human capital that would increase

productivity in the local district-municipalities with

moderate levels of inequality. This argument is in line

with the theory of labour migration which shows that

migration and location choice decisions are driven by

the behaviour of individuals or households. Individ-

uals seek to maximize their lifetime utility, which is a

function of income and other location attributes such

as quality of life. In his study, Todaro (1969)

underlines the importance of income disparities

between regions as the key determinant of rural–urban

migration. In fact, this is related to the traditional

hypothesis that the movement of individuals is a result

of job searching. Given the positive effect of the

spatially lagged Gini variable on local TFP and the

explanation assigned to it, reveals the reason for

district-municipalities located in Gauteng and the

Western Cape provinces being among the most

productive in South Africa (see Table 10 in ‘‘Ap-

pendix 1’’).

Furthermore, the result of the last spatially lagged

independent variable is that of the first period lag of

TFP. The estimated coefficient of this variable was

found positive and statistically significant at the 1 per

cent level of significance. This positive effect can

simply be explained by technological spillover effects

that occur due to cross-border aspects across district-

municipalities. However, openness to international

trade and education were positive and statistically

significant at the 10 per cent level of significance,

whereas HIV/AIDS was not statistically significant.

The result of the positive effect of trade openness on

TFP is well recognized in many countries. For

instance, Yannikkaya (2003) argues that international

trade offers access for a country to technologically

advance and make structural changes. This reasoning

is reinforced by the proponents of trade liberalization,

who consider international trade as an opportunity for

a specific country to improve efficiency and specialize

in specific products (Balassa 1965). The results of the

positive effect of trade openness on TFP are in line

with those of Bonga-Bonga and Phume (2018) who

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also found that trade openness enhances TFP in South

Africa. In order to maintain these productivity gains in

district-municipalities located in Gauteng and Wes-

tern Cape, governments need to maintain their current

environmental governance status. They need also to

continue the optimization of the industrial structure,

provide good and efficient basic public services and

maximize the social welfare.

Table 6 presents the results of the calculated

cumulative marginal effects. These were calculated

according to Lesage and Peace (2009), using the

estimated coefficient of the temporal SDM-FE, as

reported in Table 5. Table 5 also shows that the

estimated coefficient of Gini is �0:743 with a level of

significance of 1 per cent, and the elastic hysteresis

estimated coefficient of 0.615 with a level of signif-

icance of 1 per cent. In this case, both the direct and

indirect effects were found to be statistically signif-

icant, implying that if income inequality increases in

one local district-municipality by 1 per cent, TFP will

decrease by approximately �0:743 per cent in that

specific local district-municipality, and increase by

0.436 per cent in the neighbouring district-municipal-

ities. Thus, an increase in income inequality was found

to be detrimental to local district-municipalities TFP.

However, the influence of income inequality was

found to be obvious in neighbouring district-munic-

ipalities, producing positive effects on TFP.

The first period lag of TFP was also found to be

related to the current level of TFP in local district-

municipalities, and having more impact in neighbour-

ing district-municipalities in South Africa. According

to Table 5, the estimated elasticity coefficient of the

first period lag of TFP is 0.251, with a level of

significance of 1 per cent. Moreover, the estimated

elastic hysteresis passed the significance test, suggest-

ing that spillover effects are highly significant.

According to the results of the direct and indirect

effects in Table 6, if the past values of TFP change

positively by 1 per cent in local district-municipalities,

the current value of TFP in that district-municipality

will increase by 0.251 per cent, and current values of

TFP in neighbouring district-municipalities will sig-

nificantly increase by 0.607 per cent.

Finally, openness to international trade, HIV/AIDS

and education were found to have direct effects only

on TFP, because the estimated Eq. (8) did not include

the spatial lag of these three variables. The non-

inclusion of these spatially lagged terms is explained

by the preliminary analysis of their geographical

dependence showing that they were not spatially

clustered.

In sum, it is important to note that spatial econo-

metrics reveal that an increase in income inequality in

local district-municipalities has a negative and statis-

tically significant effect (direct effects) on local

conditions of TFP. In addition, it also shows that an

increase in the levels of inequality in the neighbouring

district-municipalities produces positive and statisti-

cally significant effects (indirect effects) on local

conditions of TFP. Analysis of the results indicates

that these negative effects are more pronounced in

district-municipalities where there is a lesser concen-

tration of economic activity, possibly due to historical

factors. In this regard, Todesa and Turok (2018)

indicate that during apartheid, spatial targeting was

highly instrumental in creating social divisions, at

considerable financial cost. Since the end of the

apartheid regime, there has been much experimenta-

tion with spatial initiatives, but without any relevant

overarching policy framework. Todesa and Turok

(2018) show two cautionary conclusions that can be

drawn from these spatial initiatives. The first is that

there is a high risk of excessive spending in marginal

locations in cases where political pressures are strong,

economic discipline is lacking, and public institutions

are weak. The second is that place-based policies have

potential but necessitate stronger horizontal and

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vertical policy alignment to stand any chance of

tackling engrained spatial divides. Following this line

of thought, Nel (1994) shows that from 1940–1994,

South Africa was involved in regional development

policies that were aimed at producing industrial

development in the most marginalized areas, such as

those within apartheid’s ‘‘homelands’’. When the

South African government introduced the apartheid

regime, an acknowledged system of racial segregation

led to three and half million black Africans being

relocated to ‘‘self-governing homelands’’. Over time,

these ‘‘homeland’’ regions became economically

deprived. Based on this history, we concluded that

these negative effects of income inequality can be seen

as a persistent outcome of earlier experiences of failed

regional development policies.

In order to mitigate these negative effects, novel

regional economic development policies need to be

reimagined in South Africa. Such policies have

recently been acknowledged as important strategies

for reducing regional income disparities among indi-

viduals in both developed and developing regions, and

also as being crucial for the distribution of economic

activities and growth across regions (Neumark and

Table 7 Results of Dynamic Fixed and Random-effects MLE (spatial weight: contiguity)

VARIABLES Temporal SDM-FE (1) Temporal SDM-FE (2) Temporal SDM-RE (3) Temporal SDM-RE (4)

lnGini - 0.474** - 0.472** - 0.457** - 0.434**

(0.199) (0.199) (0.184) (0.184)

lnlag1TFP 0.270*** 0.270*** 0.301*** 0.298***

(0.0297) (0.0298) (0.0287) (0.0288)

lnTrade – 0.0260 – 0.0193*

(0.0167) (0.0107)

lnHIV/AIDS – - 0.00365 – - 0.0221

(0.0191) (0.0137)

lnEDUCAT – 0.0473 – 0.00298

(0.0288) (0.0139)

W * lnGini (h2) 0.310*** 0.223*** 0.401*** 0.370***

(0.0252) (0.0258) (0.187) (0.226)

W * lnlag1TFP (h1) 0.356*** 0.342*** 0.327*** 0.323***

(0.055) (0.055) (0.054) (0.054)

W * lnTFP ðqÞ 0.249*** 0.235*** 0.238*** 0.231***

(0.047) (0.047) (0.046) (0.046)

Observations 1092 1092 1092 1092

Number of groups 52 52 52 52

Pseudo R2 0.309 0.313 0.308 0.313

Model selection tests

Log likelihood -850.60 -848.08 -880 -878.24

AIC 1713.21 1714.16 1775.59 1776.485

SBIC 1743.18 1759.12 1810.56 1826.44

Wald v2 model sign 488.92 495.85 529.91 537.26

Wald test spatial term 171.66 142.90 159.96 148.37

r2e [0.000] [0.000] [0.000] [0.000]

F-test joint sign – 5.06 – 7.11*

[0.167] [0.068]

Hausman test (v2) 16.09***

SDM-FE (2) v/s SDM- RE (4) 52 [0.006]

Standard errors in (), ***p\ 0.01, **p\ 0.05, *p\ 0.1, P-values in [], Hausman testH0: Temporal SDM-RE is consistent

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Simpson 2015). These policies must include, for

instance, a relevant public transfer of funds to boost

the development of marginalised district-municipali-

ties mostly located in the provinces of Limpopo, North

West, Eastern Cape Free State, Kwazulu-Natal and

Northern Cape. This transfer can take the form of

investment in public infrastructure (roads, hospitals

and schools) or/and fiscal tax incentives. Moreover, in

the case of South Africa, such regional policies might

yield substantial effects through changes in the

institutional environment of targeted district-munici-

palities. This means that most regional programmes

should include changes in the labour regulations of

these targeted district-municipalities. The key objec-

tive of changing labour regulations is to attract

manufacturing firms in marginalised district-munici-

palities and kick-start the agglomeration processes

that will certainly create long-term positive economic

effects in these particular district-municipalities.

Robustness check

When the spatial weighting matrix is defined to

represent the spillover effects based on an economic

distance approach, as in the case of this study, it can be

found to be time-varying, and quite often endogenous,

in spatial panel data models (Liu and Bi 2019). In most

cases, the estimation process leads to estimation bias.

Table 8 Model

comparison: Fixed-effects

SDM-FE versus SAR-FE

and SEM-FE

Standard errors in

parentheses, *** p\ 0.01,

** p\ 0.05, * p\ 0.1

LR denotes Likelihood ratio

VARIABLES Temporal SDM-FE Temporal SAR-FE Temporal SEM-FE

lnGini - 0.743*** - 0.388*** - 0.604***

(0.199) (0.129) (0.184)

lnlag1TFP 0.251*** 0.284*** 0.268***

(0.0300) (0.0286) (0.0309)

lnTrade 0.0271* 0.0289* 0.0265

(0.0165) (0.0165) (0.0167)

lnHIV/AIDS 0.00304 - 0.00291 0.000877

(0.0190) (0.0190) (0.0188)

lnEDUCAT 0.0521* 0.0725*** 0.0971**

(0.0281) (0.0275) (0.0379)

W * lnGini(h2) 0.615*** – –

(0.296)

W * lnlag1TFP(h1) 0.340*** – –

(0.094)

W * lnTFP (q) 0.401*** 0.615*** –

(0.081) (0.046)

Lambda (k) 0.708***

(0.047)

Wald test spatial term 172.08*** 174.57***

H0 : q ¼ 0 [0.000] [0.000]

LR test on rho (v2) 21.27*** 18.77*** –

H0 : q ¼ 0 [0.000] [0.000]

LR test on lambda (v2) – – 42.43***

H0 : k ¼ 0 [0.000]

Observations 1092 1092 1092

Number of groups 52 52 52

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Qu and Lee (2015) used the law of large numbers

(LLN) for the spatial near-epoch dependence (SNED)

to overcome the endogeneity bias problem. Moreover,

in dealing with situations of endogenous spatial

dynamics, they established an asymptotic distribution

of quasi-maximum likelihood (QML) estimators

under the framework of spatial-time LLN and the

central limit theorem. Consequently, an alternative

specification of the spatial weighting matrix should be

designed and tested to establish whether the estimates

will still be significant and stable. Zhou et al. (2019)

contend that the relevance and validity of spatial

regressions depend on the nature and definition of the

spatial weighting matrix. In addition, the authors

indicate that it is a sign of robustness if the regression

results are still significant with an alternative defini-

tion and specification of the spatial weighting matrix.

To ensure that the results in Table 5 were statistically

robust, we performed supplementary regressions using

the first order contiguity matrix. The results are

reported in Table 7.

Compared to Table 5, we found that the results of

the variables of our key interest (current level of Gini,

the spatially lagged values of Gini, TFP, and the

spatially lagged values of the first period lag of TFP) in

Table 7, remained statistically significant at the 1 per

cent significance level, and had the exact expected

signs. As in Table 5, all the tests applied for model

selection between the temporal SDM-FE and SDM-

RE were found to be in favour of the temporal SDM-

FE. Based on these robust regressions, we concluded

that our estimation results were consistent and relevant

for policy design.

We then turned our focus to further testing whether

the temporal SDM-FE is indeed the most appropriate

model compared to the temporal SAR-FE and SEM-

FE. Although the estimation results could be quite

similar for each specification, model comparison is

indispensable in choosing the correct specification.

We estimated the temporal SAR-FE using Eq. (8),

while the temporal SEM-FE was estimated using

Eqs. (6 and 7). As mentioned earlier, we used the

Likelihood ratio and Wald test in assessing whether

the temporal SDM-FE could be reduced to a temporal

spatial lag (H0 : h1 ¼ h2 ¼ 0) or spatial error (H0 :h1;2?qbj=0) model. As shown by LeSage and Pace

(2009), these two tests produce almost the same

results. The results from this study are reported in

Table 8. According to the results of both tests, the first

null hypothesis is statistically and significantly

rejected at the 5 per cent level of significance. This

rejection suggests that the temporal spatial lag model

is not the most suitable specification for the data of this

work. Additionally, the results of both tests indicate

that the second null hypothesis could be also rejected,

which means that the temporal spatial error model is

also not appropriate. In sum, both test (LR and Wald)

results show that the temporal SDM-FE is the most

suitable specification for this relationship under study.

Conclusions

This study attempted to bring clarity to the question of

whether increasing income inequality enhances Total

Factor Productivity (TFP) in South Africa, as sup-

ported by the skill-biased technological change argu-

ment. Based on the spatiotemporal evolution of

income inequality and factor productivity across

South Africa’s 52 district-municipalities, this paper

applied the dynamic spatial Durbin model (a spatial

panel econometric model), to quantitatively examine

the impact of income inequality and its spillover

effects on TFP. The use of spatial econometrics in this

analysis allowed us to reach some intuitive and robust

conclusions, in contrast to the uncertain and inaccurate

conclusions reached without the use of spatial meth-

ods (OLS, Fixed and Random Effects and system

GMM). First and most essential, we found substantial

evidence of positive spatial clustering of TFP across

district-municipalities in South Africa. This evidence

occurs in the spatial regression results showing the

positive and significant coefficient of q and k (see

Table 8), when all the control variables and a temporal

one-period lag of TFP are included. This evidence can

also be seen in the plots of the Moran’s Ii. To the best

of our knowledge, such strong and robust evidence of

TFP dynamics has not been presented to date.

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GeoJournal

Furthermore, our results also show that an increase

in income inequality in local district-municipalities

has a negative and statistically significant effect (direct

effects) on TFP. The negative results are supported by

the negative link that exist between inequality and

growth via the channel of political instability. In other

words, the negative results of inequality indicate that

income inequality foster political instability, which in

turn harms productivity and economic growth.

Besides, an increase in the levels of inequality in the

neighbouring district-municipalities was found to be

associated with the positive and statistically signifi-

cant effects (indirect effects) on TFP in local district-

municipalities. These results imply that the negative

effects of income inequality on productivity and

growth among adjacent regions is not simply an

intuitive theory, but seems to be a fundamental fact of

economic globalization and space relations. By con-

necting the result of the negative effects of income

inequality on TFP to the skill-biased technological

change (SBTC) argument, we then rejected the null

hypothesis that states that productivity would drop if

earnings/income inequality were considerably

reduced.

Policy-wise, we have suggested that new regional

economic development policies should be redefined

by the government in order to alleviate the negative

effects of income inequality on TFP in local district-

municipalities. We proposed that those policies should

be put in place in the aim of attracting industrial firms

in marginalized district-municipalities so that a quick

start of agglomeration processes that will certainly

create long term positive economic effects in deprived

district-municipalities be realized. In terms of the

positive spatial spillover effects of income inequality

in different local district-municipalities, we proposed

that governments need to maintain their current

environmental governance status. They need also to

continue the optimization of the industrial structure,

provide good and efficient basic public services and

maximize the social welfare.

The results revealed some interesting additional

findings, which deserve further study. In particular, we

found that income inequality has positive and statis-

tically significant effects on political instability in

South Africa. This finding indicates that polities that

have high income inequality levels are less stable com-

pared to those with lower levels of income inequality.

Despite the many aspects still to be addressed about

spatial factors in the relationship between income

inequality and TFP, this study put forward the

usefulness of spatial econometrics by providing

empirical evidence of the effects of inequality on

TFP, and by indicating the path toward a clear

understanding of the role of local and regional

interactions. We believe that the findings of this study

will be helpful to scholars and policymakers in

strategizing and designing policy that will reduce

inequality across district-municipalities and among

individuals, and that it will enhance productivity and

growth in South Africa.

Author contributions Kamanda Delphin Espoir conceived the

key ideas for this research paper. He collected and analyzed the

data. He also worked on the introduction, literature review,

methodology, results and conclusion. Nicholas Ngepah worked

on the technical oversight, quality control and writing the policy

discussion. The two authors have read and approved the final

version of this manuscript.

Compliance with ethical standards

Conflict of interest The authors declare no conflict of interest.

The School of Economics and Econometrics of the University of

Johannesburg had no role in the design of the study; in the

collection, analyses, or interpretation of data; in the writing of

the manuscript, and in the decision to publish the results.

Appendix 1

See Tables 9, 10 and Fig. 4.

Table 9 Regression results of Inequality and political

instability

VARIABLES (1) (2)

Lnpubviolence Lnpubviolence

lag1lnpubviolence 0.80850 –

(0.022)

lnGini 8.501*** 37.390***

(1.477) (1.837)

Constant 16.67* 21.54***

(7.562) (0.0361)

R-squared 0.694 0.284

Standard errors in parentheses ***p\ 0.01, **p\ 0.05,

*p\ 0.1, lnpubviolence is the log of number of public

violence

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Table 10 Cross-districts average TFP score and income inequality (time period: 1995 to 2015)

Province District-municipality Average TFP score Average TFP score Average Gini coefficient

Gauteng City of Johannesburg 0.82 0.62

City of Tshwane 0.74 0.61

Sedibeng 1.20 0.61

West Rand - 0.14 0.58

Ekurhuleni 0.99 0.60

Western Cape City of Cape Town 0.87 0.59

West Coast 0.90 0.60

Cape Winelands 0.86 0.58

Overberg 0.81 0.58

Eden 0.82 0.59

Central Karoo 0.07 0.60

North West Bojanala 0.15 0.58

Ngaka Modiri Molema 0.81 0.60

Dr Ruth Segomotsi Mompati 0.63 0.59

Dr Kenneth Kaunda - 0.13 0.59

Northern Cape John Taolo Gaetsewe 0.83 0.62

Namakwa 0.76 0.61

Pixley ka Seme 0.47 0.63

Siyanda 0.69 0.63

Frances Baard 0.67 0.62

Limpopo Mopani 0.59 0.63

Vhembe 0.31 0.63

Capricorn 0.59 0.61

Waterberg 0.80 0.60

Sekhukhune 0.56 0.63

Kwazulu Natal UGu 0.98 0.58

UMgungundlovu 1.08 0.58

UMkhanyakude 0.34 0.59

UMzinyathi 0.59 0.58

UThukela 1.00 0.59

UThungulu 1.18 0.59

iLembe 0.38 0.59

Sisonke 0.67 0.59

eThekwini 0.27 0.58

Free State Xhariep 0.69 0.62

Lejweleputswa - 0.31 0.61

Thabo Mofutsanyane 0.88 0.62

Fezile Dabi 1.25 0.63

Mangaung 0.32 0.61

Eastern Cape Buffalo City 1.29 0.63

Cacadu 0.97 0.61

Amathole 0.35 0.64

Chris Hani 0.43 0.64

Joe Gqabi 0.44 0.65

O.R.Tambo 0.30 0.64

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Appendix 2

See Table 11.

Fig. 4 Relationship

between income inequality

and political instability

across district-

municipalities in South

Africa

Table 10 continued

Province District-municipality Average TFP score Average TFP score Average Gini coefficient

Alfred Nzo 0.18 0.65

Nelson Mandela Bay 1.61 0.60

Mpumalanga Gert Sibande 0.97 0.62

Nkangala 0.61 0.61

Ehlanzeni 0.62 0.62

Source: Authors own calculations

Table 11 Moran’s Ii for Residual of the TFP regression, by district-municipality

District-municipality Ii Sd Iið Þ Z � stat p� value�

Alfred Nzo - 0.027 0.120 - 0.063 0.950

Amajuba 0.017 0.101 0.365 0.715

Amathole - 0.038 0.179 - 0.103 0.918

Bojanala 0.292 0.112 2.792 0.005

Buffalo City 0.050 0.186 0.372 0.710

Cacadu 0.161 0.102 1.769 0.077

Cape Winelands 0.387 0.157 2.589 0.010

Capricorn 0.103 0.107 1.147 0.251

Central Karoo - 0.110 0.101 - 0.899 0.368

Chris Hani - 0.002 0.098 0.180 0.857

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Table 11 continued

District-municipality Ii Sd Iið Þ Z � stat p� value�

City of Cap Town 0.350 0.151 2.450 0.014

City of Johannesburg - 0.002 0.173 0.103 0.918

City of Tshwane 0.025 0.130 0.343 0.731

Dr Kenneth Kaunda 0.204 0.096 2.323 0.020

Dr Ruth Segomotsi Mompati 0.483 0.088 5.740 0.000

Eden 0.142 0.111 1.452 0.146

Ehlanzeni 0.044 0.094 0.675 0.500

Ekurhuleni - 0.009 0.154 0.067 0.946

eThekwini 0.112 0.143 0.921 0.357

Fezile Dabi - 0.144 0.104 -1.200 0.230

Frances Baard 0.186 0.077 2.683 0.007

Gert Siyanda - 0.000 0.093 0.208 0.835

Greater Sekhukhune 0.029 0.106 0.462 0.644

iLembe 0.124 0.145 0.988 0.323

Joe Gqabi 0.009 0.087 0.326 0.745

John Taolo Gaetsewe 0.308 0.089 3.694 0.000

Lejweleputswa - 0.080 0.087 - 0.689 0.491

Mangaung 0.028 0.097 0.492 0.623

Mopani 0.030 0.112 0.438 0.662

Namakwa - 0.094 0.092 - 0.810 0.418

Nelson Mandela Bay 0.207 0.107 2.129 0.033

Ngaka Modiri Molema 0.525 0.091 6.002 0.000

Nkangala 0.050 0.108 0.650 0.515

O.R. Tambo - 0.033 0.108 - 0.125 0.901

Overberg 0.380 0.154 2.585 0.010

Pixley ka Seme - 0.026 0.063 - 0.098 0.922

Sedibeng - 0.046 0.156 - 0.166 0.868

Sisonke - 0.005 0.128 0.117 0.907

Siyanda 0.149 0.070 2.405 0.016

Thabo Mofutsanyane 0.040 0.078 0.768 0.443

UGu 0.049 0.127 0.540 0.589

UMgungundlovu 0.058 0.130 0.601 0.548

UMkhanyakude - 0.031 0.105 - 0.106 0.916

UMzinyathi - 0.021 0.122 - 0.010 0.992

UThukela 0.031 0.102 0.496 0.620

UThungulu 0.052 0.134 0.539 0.590

Vhembe 0.121 0.115 1.225 0.221

Waterberg 0.005 0.096 0.255 0.798

West Coast 0.191 0.125 1.689 0.091

West Rand 0.004 0.156 0.153 0.878

Xhariep 0.000 0.093 0.216 0.829

Zululand - 0.009 0.116 0.088 0.930

*2-tail test; bold italic indicate significant positive spatial clustering.

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